Free access
Issue
ESAIM: COCV
Volume 12, Number 3, July 2006
Page(s) 371 - 397
DOI http://dx.doi.org/10.1051/cocv:2006012
Published online 20 June 2006
  1. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. [CrossRef] [MathSciNet]
  2. G. Allaire, Homogenization of the unsteady Stokes equations in porous media, in Progress in Partial Differential Equations: Calculus of Variations, Applications, C. Bandle Ed. Longman, Harlow (1992) 109–123.
  3. G. Allaire, Shape Optimization by the Homogenization Method. Springer, New York (2002).
  4. G. Allaire and M. Briane, Multiscale convergence and reiterated homogenization. Proc. Roy. Soc. Edinburgh A 126 (1996) 297–342.
  5. T. Arbogast, J. Douglas and U. Hornung, Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal. 21 (1990) 823–836. [CrossRef] [MathSciNet]
  6. J.M. Ball and F. Murat, Remarks on Chacon's biting lemma. Proc. Amer. Math. Soc. 107 (1989) 655–663. [MathSciNet]
  7. G. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978).
  8. A. Bourgeat, S. Luckhaus and A. Mikelić, Convergence of the homogenization process for a double-porosity model of immiscible two-phase flow. SIAM J. Math. Anal. 27 (1996) 1520–1543. [CrossRef] [MathSciNet]
  9. A. Braides and A. Defranceschi, Homogenization of Multiple Integrals. Oxford University Press, Oxford (1998).
  10. J.K. Brooks and R.V. Chacon, Continuity and compactness of measures. Adv. Math. 37 (1980) 16–26. [CrossRef]
  11. J. Casado-Diaz and I. Gayte, A general compactness result and its application to two-scale convergence of almost periodic functions. C. R. Acad. Sci. Paris, Ser. I 323 (1996) 329–334.
  12. J. Casado-Diaz and I. Gayte, The two-scale convergence method applied to generalized Besicovitch spaces. R. Soc. Lond. Proc., Ser. A 458 (2002) 2925–2946.
  13. J. Casado-Diaz, M. Luna-Laynez and J.D. Martin, An adaptation of the multi-scale method for the analysis of very thin reticulated structures. C. R. Acad. Sci. Paris, Ser. I 332 (2001) 223–228.
  14. A. Cherkaev, R. Kohn Eds., Topics in the Mathematical Modelling of Composite Materials. Birkhäuser, Boston (1997).
  15. D. Cioranescu, A. Damlamian and G. Griso, Periodic unfolding and homogenization. C.R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104.
  16. D. Cioranescu and P. Donato, An Introduction to Homogenization. Oxford Univ. Press, New York (1999).
  17. C. Conca, J. Planchard and M. Vanninathan, Fluids and Periodic Structures. Wiley, Chichester and Masson, Paris (1995).
  18. N. Dunford and J. Schwartz, Linear Operators. Vol. I. Interscience, New York (1958).
  19. V.V. Jikov, S.M. Kozlov and O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals. Springer, Berlin.
  20. M. Lenczner, Homogénéisation d'un circuit électrique. C.R. Acad. Sci. Paris, Ser. II 324 (1997) 537–542.
  21. M. Lenczner and G. Senouci, Homogenization of electrical networks including voltage-to-voltage amplifiers. Math. Models Meth. Appl. Sci. 9 (1999) 899–932. [CrossRef]
  22. J.L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Vol. I. Springer, Berlin, 1972.
  23. D. Lukkassen, G. Nguetseng and P. Wall, Two-scale convergence. Int. J. Pure Appl. Math. 2 (2002) 35–86. [MathSciNet]
  24. F. Murat and L. Tartar, H-convergence. In [14], 21–44.
  25. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608–623. [CrossRef] [MathSciNet]
  26. G. Nguetseng, Asymptotic analysis for a stiff variational problem arising in mechanics. SIAM J. Math. Anal. 21 (1990) 1394–1414. [CrossRef] [MathSciNet]
  27. G. Nguetseng, Homogenization structures and applications, I. Zeit. Anal. Anwend. 22 (2003) 73–107. [CrossRef]
  28. O.A. Oleĭnik, A.S. Shamaev and G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization. North-Holland, Amsterdam (1992).
  29. E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory. Springer, New York (1980).
  30. L. Tartar, Course Peccot. Collège de France, Paris (1977). (Unpublished, partially written in [24]).
  31. L. Tartar, Mathematical tools for studying oscillations and concentrations: from Young measures to H-measures and their variants, in Multiscale Problems in Science and Technology. N. Antonić, C.J. van Duijn, W. Jäger, A. Mikelić Eds. Springer, Berlin (2002) 1–84.
  32. A. Visintin, Vector Preisach model and Maxwell's equations. Physica B 306 (2001) 21–25. [CrossRef]
  33. A. Visintin, Some properties of two-scale convergence. Rendic. Accad. Lincei XV (2004) 93–107.
  34. A. Visintin, Two-scale convergence of first-order operators. (submitted)
  35. E. Weinan, Homogenization of linear and nonlinear transport equations. Comm. Pure Appl. Math. 45 (1992) 301–326. [CrossRef] [MathSciNet]
  36. V.V. Zhikov, On an extension of the method of two-scale convergence and its applications. Sb. Math. 191 (2000) 973–1014. [CrossRef] [MathSciNet]